{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 岭回归 Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "x = np.random.uniform(-3.0, 3.0, size=100)\n",
    "X = x.reshape(-1, 1)\n",
    "y = 0.5 * x + 3 + np.random.normal(0, 1, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "def PolynomialRegression(degree):\n",
    "    return Pipeline([\n",
    "        (\"poly\", PolynomialFeatures(degree=degree)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "        (\"lin_reg\", LinearRegression())\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "np.random.seed(666)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "167.9401085999025"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "poly_reg = PolynomialRegression(degree=20)\n",
    "poly_reg.fit(X_train, y_train)\n",
    "\n",
    "y_poly_predict = poly_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y_poly_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[ 0.00000000e+00  4.51420572e-01  2.33356109e+01  1.42846232e+01\n -6.53846205e+02 -2.53385003e+02  7.60081201e+03  2.36383160e+03\n -4.66569540e+04 -1.22026494e+04  1.67921957e+05  3.63834773e+04\n -3.72244181e+05 -6.41186496e+04  5.14730775e+05  6.58881348e+04\n -4.32752964e+05 -3.64946916e+04  2.02479125e+05  8.42103402e+03\n -4.04490051e+04]\n"
    }
   ],
   "source": [
    "# 观察可知20维的多项式回归中，系数太大了\n",
    "# 因为多项式回归的目标是使MSE尽可能的小。但是会使θ变大\n",
    "# 所以此时需要加入模型正则化，改变目标函数\n",
    "# 目标函数加入θ的平方和，使得θ变大的时候目标函数会变大\n",
    "# θ0不需要，因为θ0不是任何X的系数，对函数没有影响\n",
    "print(poly_reg[\"lin_reg\"].coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "X_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "y_plot = poly_reg.predict(X_plot)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(X_plot[:,0], y_plot, color='r')\n",
    "plt.axis([-3, 3, 0, 6])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def plot_model(model):\n",
    "    X_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "    y_plot = model.predict(X_plot)\n",
    "\n",
    "    plt.scatter(x, y)\n",
    "    plt.plot(X_plot[:,0], y_plot, color='r')\n",
    "    plt.axis([-3, 3, 0, 6])\n",
    "    plt.show()\n",
    "\n",
    "plot_model(poly_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用岭回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# α使新的超参数。α=0的时候没有加入模型正则化，α如果特别大的时候目标函数的优化任务就是让每一个θi都极可能小\n",
    "# 实际是想让MSE和θ平方和尽可能平衡\n",
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def RidgeRegression(degree, alpha):\n",
    "    return Pipeline([\n",
    "        (\"poly\", PolynomialFeatures(degree=degree)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "        (\"ridge_reg\", Ridge(alpha=alpha))\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.3233492754136291"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "# 因为θ会变得很大，所以α取比较小的值也行\n",
    "ridge1_reg = RidgeRegression(20, 0.0001)\n",
    "ridge1_reg.fit(X_train, y_train)\n",
    "\n",
    "y1_predict = ridge1_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y1_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_model(ridge1_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.1888759304218461"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "ridge2_reg = RidgeRegression(20, 1)\n",
    "ridge2_reg.fit(X_train, y_train)\n",
    "\n",
    "y2_predict = ridge2_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y2_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_model(ridge2_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.3196456113086197"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "ridge3_reg = RidgeRegression(20, 100)\n",
    "ridge3_reg.fit(X_train, y_train)\n",
    "\n",
    "y3_predict = ridge3_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y3_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_model(ridge3_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.8408455590998372"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "ridge4_reg = RidgeRegression(20, 10000000)\n",
    "ridge4_reg.fit(X_train, y_train)\n",
    "\n",
    "y4_predict = ridge4_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y4_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_model(ridge4_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[0.00000000e+00 5.36901360e-06 1.19754760e-06 4.77098756e-06\n 1.00698099e-06 4.23046101e-06 9.16406798e-07 3.86509084e-06\n 9.06192581e-07 3.61690719e-06 9.44330291e-07 3.44313395e-06\n 1.00860201e-06 3.31693796e-06 1.08565371e-06 3.22165048e-06\n 1.16762935e-06 3.14677927e-06 1.24989992e-06 3.08560039e-06\n 1.32973897e-06]\n"
    }
   ],
   "source": [
    "# θ基本为0了\n",
    "print(ridge4_reg[\"ridge_reg\"].coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.8 64-bit ('anaconda': conda)",
   "language": "python",
   "name": "python36864bitanacondaconda085db2e8b14649f4b32196068f7124e9"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}